Question

Question #063c7

Answer 1

`n = 9`

Explanation:

We know that

`pi/2-(4pi)/9=pi/18` so

`[(sin(pi/18) -sin((4pi)/9)), (sin((4pi)/g) " "sin(pi/18)) ]=[(sin(pi/2-(4pi)/9),-sin((4pi)/9)),(sin((4pi)/9),sin(pi/2-(4pi)/9))] = [(cos((4pi)/9),-sin((4pi)/9)),(sin((4pi)/9),cos((4pi)/9))] =R((4pi)/9)`

Here `R(cdot)` represents a rotation. The question now is:

How apart we are from `2kpi`? Because `R(2kpi)=I_2,k=0,1,2,cdots` so from

`2kpi=n(4pi)/9` we obtain

`k = 2(n/9)` so `n=9`